arXiv subjects

Roope Uola

Publications and source records attributed to Roope Uola.

At least 37 records · Page 2Linked to original sources

arXiv2023

Barycentric decomposition for quantum instruments

We present a barycentric decomposition for quantum instruments whose output space is finite-dimensional and input space is separable. As a special case, we obtain a barycentric decomposition for channels between such spaces and for normalized positive-operator-valued measures in separable Hilbert spaces. This extends the known results by Ali and Chiribella et al. on decompositions of quantum measurements, and formalises the fact that every instrument between finite-dimensional Hilbert spaces can be represented using only finite-outcome instruments.

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arXiv2023

Quantifying the high-dimensionality of quantum devices

We introduce a measure of average dimensionality (or coherence) for high-dimensional quantum devices. This includes sets of quantum measurements, steering assemblages, and quantum channels. For measurements and channels, our measure corresponds to an average compression dimension, whereas for quantum steering we get a semi-device independent quantifier for the average entanglement dimensionality known as the Schmidt measure. We analyse the measure in all three scenarios. First, we show that it can be decided via semi-definite programming for channels and measurements in low-dimensional systems. Second, we argue that the resulting steering measure is a high-dimensional generalisation of the well-known steering weight. Finally, we analyse the behaviour of the measure in the asymptotic setting. More precisely, we show that the asymptotic Schmidt measure of bipartite quantum states is equal to the entanglement cost and show how the recently introduced entanglement of formation for steering assemblages can be related to our measure in the asymptotic case.

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arXiv2023

Unlimited One-Way Steering

This work explores the asymmetry of quantum steering in a setup using high-dimensional entanglement. We construct entangled states with the following properties: $(i)$ one party (Alice) can never steer the state of the other party (Bob), considering the most general measurements, and $(ii)$ Bob can strongly steer the state of Alice, demonstrating genuine high-dimensional steering. In other words, Bob can convince Alice that they share an entangled state of arbitrarily high Schmidt number, while Alice can never convince Bob that the state is even simply entangled. In this sense, one-way steering can become unlimited. A key result for our construction is a condition for the joint measurability of all high-dimensional measurements subjected to the combined effect of noise and loss, which is of independent interest.

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arXiv2023

Incompatible measurements in quantum information science

Some measurements in quantum mechanics disturb each other. This has puzzled physicists since the formulation of the theory, but only in recent decades has the incompatibility of measurements been analyzed in depth and detail, using the notion of joint measurability of generalized measurements. In this Colloquium joint measurability and incompatibility are reviewed from the perspective of quantum information science. The Colloquium starts by discussing the basic definitions and concepts. An overview on applications of incompatibility, such as in measurement uncertainty relations, the characterization of quantum correlations, or information processing tasks like quantum state discrimination, is then presented. Finally, emerging directions of research, such as a resource theory of incompatibility as well as other concepts to grasp the nature of measurements in quantum mechanics, are discussed.

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arXiv2022

Retrievability of information in quantum and realistic hidden variable theories

We propose a generalisation of the Leggett-Garg conditions for macrorealistic behaviour. Our proposal relies on relaxing the postulate of non-invasive measurability with that of retrievability of information. This leads to a strictly broader class of hidden variable theories than those having a macrorealistic description. Crucially, whereas quantum mechanical tests of macrorealism require one to optimise over all possible state updates, for retrievability of information it suffices to use the basic Lüders state update, which is present in every quantum measurement. We show that in qubit systems the optimal retrieving protocols further relate to the fundamental precision limit of quantum theory given by Busch-Lahti-Werner error-disturbance uncertainty relations. We implement an optimal protocol using a photonic setting, and report an experimental violation of the proposed generalisation of macrorealism.

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arXiv2022

Naimark dilations of qubit POVMs and joint measurements

Measurement incompatibility is one of the cornerstones of quantum theory. This phenomenon appears in many forms, of which the concept of non-joint measurability has received considerable attention in the recent years. In order to characterise this non-classical phenomenon, various analytical and numerical methods have been developed. The analytical approaches have mostly concentrated on the qubit case, as well as to scenarios involving sets of measurements with symmetries, such as position and momentum or sets of mutually unbiased bases. The numerical methods can, in principle, decide any finite-dimensional and discrete joint measurability problem, but they naturally have practical limitations in terms of computational power. These methods exclusively start from a given set of measurements and ask whether the set possesses incompatibility. Here, we take a complementary approach by asking which measurements are compatible with a given measurement. It turns out, that this question can be answered in full generality through a minimal Naimark dilation of the given measurement: the set of interest is exactly those measurements that have a block-diagonal representation in such dilation. We demonstrate the use of the technique through various qubit examples, leading to an alternative characterisation of all compatible pairs of binary qubit measurements, which retrieves the celebrated Busch criterion. We further apply the technique to special examples of trinary and continuous qubit measurements.

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arXiv2022

Joint measurability in nonequilibrium quantum thermodynamics

In this Letter we investigate the concept of quantum work and its measurability from the viewpoint of quantum measurement theory. Very often, quantum work and fluctuation theorems are discussed in the framework of projective two-point measurement (TPM) schemes. According to a well known no-go theorem, there is no work observable which satisfies both (i) an average work condition and (ii) the TPM statistics for diagonal input states. Such projective measurements represent a restrictive class among all possible measurements. It is desirable, both from a theoretical and experimental point of view, to extend the scheme to the general case including suitably designed unsharp measurements. This shifts the focus to the question what information about work and its fluctuations one is able to extract from such generalized measurements. We show that the no-go theorem no longer holds if the observables in a TPM scheme are jointly measurable for any intermediate unitary evolution. We explicitly construct a model with unsharp energy measurements and derive bounds for the visibility that ensure joint measurability. In such an unsharp scenario a single work measurement apparatus can be constructed that allows us to determine the correct average work and to obtain free energy differences with the help of a Jarzynski equality.

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arXiv2022

Equivalence between simulability of high-dimensional measurements and high-dimensional steering

The effect of quantum steering arises from the judicious combination of an entangled state with a set of incompatible measurements. Recently, it was shown that this form of quantum correlations can be quantified in terms of a dimension, leading to the notion of genuine high-dimensional steering. While this naturally connects to the dimensionality of entanglement (Schmidt number), we show that this effect also directly connects to a notion of dimension for measurement incompatibility. More generally, we present a general connection between the concepts of steering and measurement incompatibility, when quantified in terms of dimension. From this connection, we propose a novel twist on the problem of simulating quantum correlations. Specifically, we show how the correlations of certain high-dimensional entangled states can be exactly recovered using only shared randomness and lower-dimensional entanglement. Finally, we derive criteria for testing the dimension of measurement incompatibility, and discuss the extension of these ideas to quantum channels.

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arXiv2022

Noise-Robust and Loss-Tolerant Quantum Steering with Qudits

A primary requirement for a robust and unconditionally secure quantum network is the establishment of quantum nonlocal correlations over a realistic channel. While loophole-free tests of Bell nonlocality allow for entanglement certification in such a device-independent setting, they are extremely sensitive to loss and noise, which naturally arise in any practical communication scenario. Quantum steering relaxes the strict technological constraints of Bell nonlocality by re-framing it in an asymmetric manner, thus providing the basis for one-sided device-independent quantum networks that can operate under realistic conditions. Here we introduce a noise-robust and loss-tolerant test of quantum steering designed for single detector measurements that harnesses the advantages of high-dimensional entanglement. We showcase the improvements over qubit-based systems by experimentally demonstrating detection loophole-free quantum steering in 53 dimensions through simultaneous loss and noise conditions corresponding to 14.2 dB loss equivalent to 79 km of telecommunication fibre, and 36% of white noise. We go on to show how the use of high dimensions counter-intuitively leads to a dramatic reduction in total measurement time, enabling a quantum steering violation almost two orders of magnitude faster obtained by simply doubling the Hilbert space dimension. By surpassing the constraints imposed upon the device-independent distribution of entanglement, our loss-tolerant, noise-robust, and resource-efficient demonstration of quantum steering proves itself a critical ingredient for making device-independent quantum communication over long distances a reality.

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arXiv2022

Simulability of high-dimensional quantum measurements

We investigate the compression of quantum information with respect to a given set $\mathcal{M}$ of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from $\mathcal{M}$ and an arbitrary quantum state $ρ$ are recovered exactly by first compressing $ρ$ into a lower dimensional space, followed by some quantum measurements. A full quantum compression is possible, i.e., leaving only classical information, if and only if the set $\mathcal{M}$ is jointly measurable. Our notion of simulability can thus be seen as a quantification of measurement incompatibility in terms of dimension. After defining these concepts, we provide an illustrative examples involving mutually unbiased basis, and develop a method based on semi-definite programming for constructing simulation models. In turn we analytically construct optimal simulation models for all projective measurements subjected to white noise or losses. Finally, we discuss how our approach connects with other concepts introduced in the context of quantum channels and quantum correlations.

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arXiv2021

Network Quantum Steering

The development of large-scale quantum networks promises to bring a multitude of technological applications as well as shed light on foundational topics, such as quantum nonlocality. It is particularly interesting to consider scenarios where sources within the network are statistically independent, which leads to so-called network nonlocality, even when parties perform fixed measurements. Here we promote certain parties to be trusted and introduce the notion of network steering and network local hidden state (NLHS) models within this paradigm of independent sources. In one direction, we show how results from Bell nonlocality and quantum steering can be used to demonstrate network steering. We further show that it is a genuinely novel effect, by exhibiting unsteerable states that nevertheless demonstrate network steering, based upon entanglement swapping, yielding a form of activation. On the other hand, we provide no-go results for network steering in a large class of scenarios, by explicitly constructing NLHS models.

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arXiv2021

Quantum marginal problem and incompatibility

One of the basic distinctions between classical and quantum mechanics is the existence of fundamentally incompatible quantities. Such quantities are present on all levels of quantum objects: states, measurements, quantum channels, and even higher order dynamics. In this manuscript, we show that two seemingly different aspects of quantum incompatibility: the quantum marginal problem of states and the incompatibility on the level of quantum channels are in many-to-one correspondence. Importantly, as incompatibility of measurements is a special case of the latter, it also forms an instance of the quantum marginal problem. The generality of the connection is harnessed by solving the marginal problem for Gaussian and Bell diagonal states, as well as for pure states under depolarizing noise. Furthermore, we derive entropic criteria for channel compatibility, and develop a converging hierarchy of semi-definite programs for quantifying the strength of quantum memories.

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arXiv2021

Set coherence: basis-independent quantification of quantum coherence

The coherence of an individual quantum state can be meaningfully discussed only when referring to a preferred basis. This arbitrariness can however be lifted when considering sets of quantum states. Here we introduce the concept of set coherence for characterising the coherence of a set of quantum systems in a basis-independent way. We construct measures for quantifying set coherence of sets of quantum states as well as quantum measurements. These measures feature an operational meaning in terms of discrimination games and capture precisely the advantage offered by a given set over incoherent ones. Along the way, we also connect the notion of set coherence to various resource-theoretic approaches recently developed for quantum systems.

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arXiv2021

Bounding and simulating contextual correlations in quantum theory

We introduce a hierarchy of semidefinite relaxations of the set of quantum correlations in generalised contextuality scenarios. This constitutes a simple and versatile tool for bounding the magnitude of quantum contextuality. To illustrate its utility, we use it to determine the maximal quantum violation of several noncontextuality inequalities whose maximum violations were previously unknown. We then go further and use it to prove that certain preparation-contextual correlations cannot be explained with pure states, thereby showing that mixed states are an indispensable resource for contextuality. In the second part of the paper, we turn our attention to the simulation of preparation-contextual correlations in general operational theories. We introduce the information cost of simulating preparation contextuality, which quantifies the additional, otherwise forbidden, information required to simulate contextual correlations in either classical or quantum models. In both cases, we show that the simulation cost can be efficiently bounded using a variant of our hierarchy of semidefinite relaxations, and we calculate it exactly in the simplest contextuality scenario of parity-oblivious multiplexing.

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arXiv2021

Genuine high-dimensional quantum steering

High-dimensional quantum entanglement can give rise to stronger forms of nonlocal correlations compared to qubit systems, offering significant advantages for quantum information processing. Certifying these stronger correlations, however, remains an important challenge, in particular in an experimental setting. Here we theoretically formalise and experimentally demonstrate a notion of genuine high-dimensional quantum steering. We show that high-dimensional entanglement, as quantified by the Schmidt number, can lead to a stronger form of steering, provably impossible to obtain via entanglement in lower dimensions. Exploiting the connection between steering and incompatibility of quantum measurements, we derive simple two-setting steering inequalities, the violation of which guarantees the presence of genuine high-dimensional steering, and hence certifies a lower bound on the Schmidt number in a one-sided device-independent setting. We report the experimental violation of these inequalities using macro-pixel photon-pair entanglement certifying genuine high-dimensional steering. In particular, using an entangled state in dimension $d=31$, our data certifies a minimum Schmidt number of $n=15$.

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arXiv2021

Quantum measurement incompatibility in subspaces

We consider the question of characterising the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is incompatible, one considers the set of measurements obtained by projection onto any strict subspace of fixed dimension. We identify three possible forms of incompatibility in subspaces: (i) incompressible incompatibility: measurements that become compatible in every subspace, (ii) fully compressible incompatibility: measurements that remain incompatible in every subspace, and (iii) partly compressible incompatibility: measurements that are compatible in some subspace and incompatible in another. For each class we discuss explicit examples. Finally, we present some applications of these ideas. First we show that joint measurability and coexistence are two inequivalent notions of incompatibility in the simplest case of qubit systems. Second we highlight the implications of our results for tests of quantum steering.

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arXiv2020

An operational characterization of infinite-dimensional quantum resources

Recently, various non-classical properties of quantum states and channels have been characterized through an advantage they provide in specific quantum information tasks over their classical counterparts. Such advantage can be typically proven to be quantitative, in that larger amounts of quantum resources lead to better performance in the corresponding tasks. So far, these characterizations have been established only in the finite-dimensional setting. In this manuscript, we present a technique for extending the known results to the infinite-dimensional regime. The technique relies on approximating infinite-dimensional resource measures by their finite-dimensional counterparts. We give a sufficient condition for the approximation procedure to be tight, i.e. to match with established infinite-dimensional resource quantifiers, and another sufficient condition for the procedure to match with relevant extensions of these quantifiers. We show that various continuous variable quantum resources fall under these conditions, hence, giving them an operational interpretation through the advantage they can provide in so-called quantum games. Finally, we extend the interpretation to the max relative entropy in the infinite-dimensional setting.

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arXiv2020

Experimental demonstration of robust quantum steering

We analyse and experimentally demonstrate quantum steering using criteria based on generalised entropies and criteria with minimal assumptions based on the so-called dimension-bounded steering. Further, we investigate and compare their robustness against experimental imperfections such as misalignment in the shared measurement reference frame. Whilst entropy based criteria are robust against imperfections in state preparation, we demonstrate an advantage in dimension-bounded steering in the presence of measurement imprecision. As steering with such minimal assumptions is easier to reach than fully non-local correlations, and as our setting requires very little trust in the measurement devices, the results provide a candidate for the costly Bell tests while remaining highly device-independent.

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